Discrete Math - Modular Arithmetic

hammonjj

1. The problem statement, all variables and given/known data
For which values of n≥2 does the implication:

axb=0 ⇔ a=0 or b=0

For some Zn (n should be a subscript)

NOTE: For the a x b, the x should be the x that has a circle around it. I didn't see that symbol in the "quick symbols" :)

2. Relevant equations
I know that this is true when n is a prime (answer in back of book), but I don't understand why. For example, if a=5 and b = 4, then that would also be 0 for n=5, right? Do I just not understand how to do modular arithmetic?

Thanks!

HallsofIvy

What is your definition of that symbol? I would have interpreted as a "tensor product" but that doesn't really make sense here. I suspect it is a "special operation" your text is defining for this problem.

tiny-tim

hi hammonjj!
ah, but 5 = 0